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The Lieb-Robinson bound has been a milestone in our understanding of the nonequilibrium dynamics of nonrelativistic short-range interacting quantum systems. In essence it states that the effect of a perturbation at a point A cannot be felt at another point B until a time t=r/v, with r the distance between A and B and v a characteristic velocity in the system. Even though causality is not strictly imposed on the model, it emerges as a mere consequence of the short-range nature of interactions, thereby giving rise to an effective light cone.
Recent advances in in cold-atom and trapped-ion experiments have made it possible to also study the behavior of long-range interacting quantum systems. As in these systems the Lieb-Robinson theorem ceases to hold, there is not much general that can be said about the rate at which correlations can travel through the system. New bounds on information propagation have been proposed, but they seem too loose to provide any significant insight into models of interest. Thus, is it really possible to transmit information superluminally in these systems? Or is some notion of causality still preserved, despite the long-range nature of interactions?
With this work we aim at providing some insight into these elementary questions by considering an exactly solvable fermionic model with pairing interactions that decay as 1/rα, known as the long-range Kitaev chain. We study the dynamics after an abrupt change of vacuum and evaluate the mutual information between two disconnected subsystems in the chain. Surprisingly, we find that by far most of the information in this model still propagates inside a well-defined light cone, even for very long-range interactions (α<1). Moreover, the crucial difference with short-range interacting models lies in the fact that, counterintuitively, the dynamics can be slowed down significantly, rather than sped up. We illustrate that, thanks to the integrability of the model, the distribution of quasiparticle group velocities is sufficient to explain these remarkable observations.
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